/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
Input TRS:
    1: from(X) -> cons(X,n__from(n__s(X)))
    2: 2ndspos(0(),Z) -> rnil()
    3: 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
    4: 2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
    5: 2ndsneg(0(),Z) -> rnil()
    6: 2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
    7: 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,activate(Z)))
    8: pi(X) -> 2ndspos(X,from(0()))
    9: plus(0(),Y) -> Y
    10: plus(s(X),Y) -> s(plus(X,Y))
    11: times(0(),Y) -> 0()
    12: times(s(X),Y) -> plus(Y,times(X,Y))
    13: square(X) -> times(X,X)
    14: from(X) -> n__from(X)
    15: s(X) -> n__s(X)
    16: activate(n__from(X)) -> from(activate(X))
    17: activate(n__s(X)) -> s(activate(X))
    18: activate(X) -> X
Number of strict rules: 18
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #2ndsneg(s(N),cons(X,Z)) -> #2ndsneg(s(N),cons2(X,activate(Z)))
   #2: #2ndsneg(s(N),cons(X,Z)) -> #activate(Z)
   #3: #square(X) -> #times(X,X)
   #4: #times(s(X),Y) -> #plus(Y,times(X,Y))
   #5: #times(s(X),Y) -> #times(X,Y)
   #6: #2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #2ndspos(N,activate(Z))
   #7: #2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #activate(Z)
   #8: #plus(s(X),Y) -> #s(plus(X,Y))
   #9: #plus(s(X),Y) -> #plus(X,Y)
   #10: #activate(n__s(X)) -> #s(activate(X))
   #11: #activate(n__s(X)) -> #activate(X)
   #12: #activate(n__from(X)) -> #from(activate(X))
   #13: #activate(n__from(X)) -> #activate(X)
   #14: #2ndspos(s(N),cons(X,Z)) -> #2ndspos(s(N),cons2(X,activate(Z)))
   #15: #2ndspos(s(N),cons(X,Z)) -> #activate(Z)
   #16: #pi(X) -> #2ndspos(X,from(0()))
   #17: #pi(X) -> #from(0())
   #18: #2ndspos(s(N),cons2(X,cons(Y,Z))) -> #2ndsneg(N,activate(Z))
   #19: #2ndspos(s(N),cons2(X,cons(Y,Z))) -> #activate(Z)
Number of SCCs: 4, DPs: 8
	SCC { #5 }
Sum... succeeded.
  negrecip(x1)		w: (0)
  s(x1)		w: (1 + x1)
  2ndspos(x1,x2)		w: (0)
  activate(x1)		w: (0)
  rnil()		w: (0)
  #plus(x1,x2)		w: (0)
  n__from(x1)		w: (0)
  square(x1)		w: (0)
  #activate(x1)		w: (0)
  #square(x1)		w: (0)
  pi(x1)		w: (0)
  rcons(x1,x2)		w: (0)
  n__s(x1)		w: (0)
  #times(x1,x2)		w: (x1)
  0()		w: (0)
  from(x1)		w: (0)
  times(x1,x2)		w: (0)
  #s(x1)		w: (0)
  2ndsneg(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #2ndspos(x1,x2)		w: (0)
  cons2(x1,x2)		w: (0)
  #from(x1)		w: (0)
  cons(x1,x2)		w: (0)
  #pi(x1)		w: (0)
  #2ndsneg(x1,x2)		w: (0)
  posrecip(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 3, DPs: 7
	SCC { #9 }
Sum... succeeded.
  negrecip(x1)		w: (0)
  s(x1)		w: (1 + x1)
  2ndspos(x1,x2)		w: (0)
  activate(x1)		w: (0)
  rnil()		w: (0)
  #plus(x1,x2)		w: (x1)
  n__from(x1)		w: (0)
  square(x1)		w: (0)
  #activate(x1)		w: (0)
  #square(x1)		w: (0)
  pi(x1)		w: (0)
  rcons(x1,x2)		w: (0)
  n__s(x1)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (0)
  from(x1)		w: (0)
  times(x1,x2)		w: (0)
  #s(x1)		w: (0)
  2ndsneg(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #2ndspos(x1,x2)		w: (0)
  cons2(x1,x2)		w: (0)
  #from(x1)		w: (0)
  cons(x1,x2)		w: (0)
  #pi(x1)		w: (0)
  #2ndsneg(x1,x2)		w: (0)
  posrecip(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 2, DPs: 6
	SCC { #11 #13 }
Sum... succeeded.
  negrecip(x1)		w: (0)
  s(x1)		w: (1)
  2ndspos(x1,x2)		w: (0)
  activate(x1)		w: (0)
  rnil()		w: (0)
  #plus(x1,x2)		w: (0)
  n__from(x1)		w: (1 + x1)
  square(x1)		w: (0)
  #activate(x1)		w: (x1)
  #square(x1)		w: (0)
  pi(x1)		w: (0)
  rcons(x1,x2)		w: (0)
  n__s(x1)		w: (1 + x1)
  #times(x1,x2)		w: (0)
  0()		w: (0)
  from(x1)		w: (0)
  times(x1,x2)		w: (0)
  #s(x1)		w: (0)
  2ndsneg(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #2ndspos(x1,x2)		w: (0)
  cons2(x1,x2)		w: (0)
  #from(x1)		w: (0)
  cons(x1,x2)		w: (0)
  #pi(x1)		w: (0)
  #2ndsneg(x1,x2)		w: (0)
  posrecip(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #11 #13
Number of SCCs: 1, DPs: 4
	SCC { #1 #6 #14 #18 }
Sum... succeeded.
  negrecip(x1)		w: (0)
  s(x1)		w: (1 + x1)
  2ndspos(x1,x2)		w: (0)
  activate(x1)		w: (1)
  rnil()		w: (0)
  #plus(x1,x2)		w: (0)
  n__from(x1)		w: (3 + x1)
  square(x1)		w: (0)
  #activate(x1)		w: (0)
  #square(x1)		w: (0)
  pi(x1)		w: (0)
  rcons(x1,x2)		w: (0)
  n__s(x1)		w: (1)
  #times(x1,x2)		w: (0)
  0()		w: (0)
  from(x1)		w: (2)
  times(x1,x2)		w: (0)
  #s(x1)		w: (0)
  2ndsneg(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #2ndspos(x1,x2)		w: (x1)
  cons2(x1,x2)		w: (21238 + x2)
  #from(x1)		w: (0)
  cons(x1,x2)		w: (1 + x2 + x1)
  #pi(x1)		w: (0)
  #2ndsneg(x1,x2)		w: (x1)
  posrecip(x1)		w: (0)
    USABLE RULES: { 15 }
    Removed DPs: #6 #18
Number of SCCs: 0, DPs: 0